Houdini Adventures

heres a cool trick i learnt regarding infinite decimal numbers - 
ie
3.711711711711711711.....

let S = 3.711711711...
S= 3 + 711/1000 + 711/1000^2 + 711/1000^3....

see the pattern - the "ratio" is 1:1000 each time, each element in the series.

therefore 1000.S = 3711 + 711/1000 + 711/1000^2 + 711/1000^3....
1000.S - S = 3711- 3    (the infinite recurring decimals subtract and are removed from the picture)

999 S = 3708

S = 3708/999 or 412/111

pretty nifty !